We close with some more general remarks on the embedding of our work
within the field of ST. The starting point of our paper was the wealth
of literature concerning ST of Brownian and Markovian systems. As
pointed out in the introduction, there have been several recent
efforts to generalize aspects of ST, particularly FRs, towards
non-Markovian systems described e.g., by GLEs. In the present work we
were asking, more generally, what can be learned when we apply the
"standard" ST scheme with notions such as entropy, heat, and
temperature to systems exhibiting anomalous dynamics, which are
"athermal" [1]} in the sense that there is no direct
relation between temperature and noise. We emphasize (again) that
such processes are by no means "exotic" mathematical artefacts, as
they are widely observed in physical and biological
experiments. In particular, they may have important applications
to better understand active matter. Our analysis shows that ST for
these processes indeed suggests new definitions for thermodynamic
quantities like temperature or heat, and a respective interpretation
of the physical contributions. We thus view our present analysis as an
important contribution to the development of ST for anomalous
dynamics.
